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Conditional Probability

Conditional Probability. M408 Probability Unit. Dependent Events – (from last time) . P(A, given that B occurred) tells us the probability that A happens, on the condition that B has happened. This is called a conditional probability . It can also be thought of as P(A, IF B happens).

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Conditional Probability

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  1. Conditional Probability M408 Probability Unit

  2. Dependent Events – (from last time) • P(A, given that B occurred) tells us the probability that A happens, on the condition that B has happened. • This is called a conditional probability. • It can also be thought of as P(A, IF B happens). We will use the notation P(A|B) to represent P(A given B)

  3. Conditional Probability – rearrange the formula from the previous slide to get a formula for the conditional. becomes

  4. ‘B’ is the event that we assume has happened. ‘A’ is the event whose probability we want to determine. A conditional statement reduces the sample space. Key phrases: given, if, on the condition of,…

  5. Ex 1 – Use the known probabilities. • a.) b.) • c.) d.) • e.) How is the prob. of Z affected if we know event Y happens? • f.) Are events X and Y independent? • g.) Are events X and Z independent?

  6. Ex 2 – Animal Hoarders My neighbor has 3 black cats, 6 white cats, 1 brown cat, 2 black dogs, 3 white dogs, 8 brown dogs, 1 black ferret, 4 white ferrets, and 2 brown ferrets. An animal escapes into my yard. Find the following probabilities. A.) P(cat) B.) P(White) C.) Prob. it is a cat, given that it is brown. D.) Prob. it is white, if it is a ferret. E.) P(Not Brown | Dog) F.) P(Not Cat | Not White)

  7. Ex 3 – Three coins are tossed. A.) Find the probability that at least two are tails, given that the 2nd coin is tails. B.) P(at least two tails | 2nd coin is heads)

  8. Ex 4 – Select one person from class at random. The probability that he/she can do a cartwheel is 0.68. The probability that he/she can do a handstandanda cartwheel is 0.40. What is the probability that he/she can do a handstand, if we know they can do a cartwheel?

  9. Ex 5 – The carnival is in town! The probability that youget sick there, given that you ride the tilt-a-whirlmore than once, is 0.84. The probability of youriding the tilt-a-whirl more than once is 0.32.What is the probability that you ride thetilt-a-whirl more than once and you get sick?

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